A mirror theorem for the mirror quintic

Lee, Yuan-Pin¹ ; Shoemaker, Mark¹

¹ Department of Mathematics, University of Utah, 155 S 1400 E Room 233, Salt Lake City, UT 84112-0090, USA

Geometry & topology, Tome 18 (2014) no. 3, pp. 1437-1483.

Résumé

The celebrated Mirror theorem states that the genus zero part of the $A$ model (quantum cohomology, rational curves counting) of the Fermat quintic threefold is equivalent to the $B$ model (complex deformation, variation of Hodge structure) of its mirror dual orbifold. In this article, we establish a mirror-dual statement. Namely, the $B$ model of the Fermat quintic threefold is shown to be equivalent to the $A$ model of its mirror, and hence establishes the mirror symmetry as a true duality.

Détail

DOI : 10.2140/gt.2014.18.1437

Classification : 14N35, 53D45
Keywords: mirror symmetry, mirror theorem

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